Results 61 to 70 of about 35,710 (245)

Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking

, 2010
We have recently solved the inverse spectral problem for integrable PDEs in arbitrary dimensions arising as commutation of multidimensional vector fields depending on a spectral parameter $\lambda$.
Bogdanov L, Bogdanov L, Dunajski M, Dunajski M Tod K P, Guil F, Kadomtsev B B, Kodama Y, Konopelchenko B, Manakov S V, Manakov S V, Manakov S V, Manakov S V Santini P M, Neyzi F, P M Santini, S V Manakov, Takasaki K Takebe T, Takasaki K Takebe T, Timman R Oswatitsch K, Zakharov V E, Zakharov V E, Zakharov V E, Zobolotskaya E A   +21 more
core   +1 more source

Remarks on control and inverse problems for PDEs

SeMA Journal
This paper deals with recent results and open questions on the control and parameter identification of systems governed by PDEs. Among them, we find a few parabolic and hyperbolic equations, sometimes in the framework of a free-boundary problem.
Emique Fernández-Cara
semanticscholar   +1 more source

DISCRETE NON-STANDARD FORMULATION OF PDE INVERSE PROBLEMS

International Journal of Numerical Methods and Applications, 2022
Abstract In this paper, we are interested in the computation of the unknown initial state for the simulation and prediction of PDE systems where the solution measures are partially known over a time interval. Such a problem is usually solved by an ill-posed optimal control problem.
Cyr S. Ngamouyih Moussata, Mahamat Saleh Daoussa Haggar, Deryl Nathan Bonazébi Yindoula, Benjamin Mampassi   +3 more
openaire   +1 more source

The Numerical Solution of Singularly Perturbed Nonlinear Partial Differential Equations in Three Space Variables: The Adaptive Explicit Inverse Preconditioning Approach

Modelling and Simulation in Engineering, 2019
Critical comments on the complexity of computational systems and the basic singularly perturbed (SP) concepts are given. A class of several complex SP nonlinear elliptic equations arising in various branches of science, technology, and engineering is ...
Anastasia-Dimitra Lipitakis
doaj   +1 more source

Consensus ADMM for Inverse Problems Governed by Multiple PDE Models

, 2021
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these large-scale inverse problems into smaller, simpler sub-problems, for which computationally efficient solvers are available ...
Lozenski, Luke, Villa, Umberto
openaire   +2 more sources

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

, 2004
The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation ...
Agranovsky M, Agranovsky M, Andersson L-E, Bers L, Courant R, Denisjuk A, Ehrenpreis L, Fawcett J A, Finch D, Flatto L, Gelfand I, Gelfand I, Gindikin S, Helgason S, Hörmander L, John F, Kruger R A, Kuchment P, Louis A K, Natterer F, Natterer F, Nilsson S, Norton S J, Norton S J, Palamodov V P, Patch S K, Quinto E T, Quinto E T, Spivak M, Xu Y, Ya V, Zobin N   +31 more
core   +2 more sources

On inverse problems for several coupled PDE systems arising in mathematical biology

Journal of Mathematical Biology, 2023
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems, we mainly consider the non-negative solutions of the coupled equations, which are consistent with realistic ...
Ming-Hui Ding, Hongyu Liu, Guang-Hui Zheng   +2 more
openaire   +3 more sources

On numerical simulation of liquid polymer moulding

Mathematical Modelling and Analysis, 2003
In this paper we consider numerical algorithms for solving the system of nonlinear PDEs, arising in modeling of liquid polymer injection. We investigate the particular case when a porous preform is located within the mould, so that the liquid polymer is ...
R. Čiegis, O. Iliev
doaj   +1 more source

Mechanistic Modeling of Continuous Lyophilization for Biopharmaceutical Manufacturing

Advanced Science, EarlyView.
This article presents the first mechanistic model for continuous lyophilization (aka freeze drying). The model accurately describes the key phenomena and critical process parameters in continuous lyophilization, which can be used for process design, optimization, and control. Results from this work can drive the transition of (bio)pharmaceutical freeze
Prakitr Srisuma, Gang Chen, Richard D. Braatz   +2 more
wiley   +1 more source

Causality-Aware Training of Physics-Informed Neural Networks for Solving Inverse Problems

Mathematics
Inverse Physics-Informed Neural Networks (inverse PINNs) offer a robust framework for solving inverse problems governed by partial differential equations (PDEs), particularly in scenarios with limited or noisy data. However, conventional inverse PINNs do
Jaeseung Kim, Hwijae Son
doaj   +1 more source